Bredon motivic cohomology of the real numbers

Abstract

Over the real numbers with $\mathbb{Z}/2-$coefficients, we compute the $C_2$-equivariant Borel motivic cohomology ring, the Bredon motivic cohomology groups and prove that the Bredon motivic cohomology ring of the real numbers is a proper subring in the $RO(C_2\times C_2)$-graded Bredon cohomology ring of a point. This generalizes Voevodsky's computation of the motivic cohomology ring of the real numbers to the $C_2$-equivariant setting. These computations are extended afterwards to any real closed field.

arXiv comment37 pages, to appear JPAA